Super Mario Bros. / Duck Hunt was one of the first for me as well. I will be forever indebted to my uncle for explaining how to beat World 4-4, the first looping castle stage, because I couldn't figure it out for the life of me. My experiences playing Mario as a child remain with me today; even now, playing on the Wii virtual console, my girlfriend seems to think that I have the entire game memorized. Unfortunately, although I've made it to the last stage, I have yet to save the princess. :-( I try to soothe my wounded ego by reminding myself that I beat The Lost Levels in Super Mario All Stars, but it just isn't the same.
I also used to play quite a few games of Mrs. Pac Man on an old arcade machine that used to be in the waiting room at my pediatrician's office. I was never very good at Pac Man, though. After three or four stages, Inky, Pinky, Blinky, and whatsis-face usually managed to gang rape me.